Can this low-light animation in Cycles be rendered sharply and in HD, and how?
To be honest, this scene is relatively light-weight already.
A single frame at 1000 samples at 50% resolution takes almost exactly 20 minutes on my CPU (a quad core intel xeon, though the clock rate is only 2.5 GHz). Naturally using a GPU (or both CPU and GPU at once) would help dramatically.
Rendering simply takes time. Even the giant renderfarms at ILM or pixar spend as much as four hours or more[better citation needed] rendering a single frame in some scenes.
If you want to render the scene exactly as it is in a short time frame, you might consider sending it off to a renderfarm such as SheepIt, a free distributed blender-specific renderfarm where blenderusers from all over the world donate and exchange their processing time.
Optimizations
For reference:
Default setup (100 samples, 40% resolution, frame 20):  1:19

As far as things you can do without changing the result go, this scene is already pretty optimized.
You can shave off a few seconds by reducing the bounces. (an optimization of a few seconds at preview resolution and samples can turn into minutes at full quality)
Reduced bounces: 0:59

Keep in mind that tile size can also have a sizable impact on rendertime, but the nature of this impact heavily depends on the scene and your hardware.

Scene changing optimizations
By using an arealamp to do the main illumination and dimming the letters, allowing the less-noisy area lamp do all the work, a lot of the noise is less noticeable. Adding a glare node helps cover the noise directly behind the letters somewhat:

Yes, the rendertime increased (thanks to the glare node), but now the result appears slightly less noisy.
Taking this to the extreme you could even make the letters visible only to the camera:

Now it's nearly at a point where you might be able to get away with 100 samples for the final render (you might still want to use 200-300 or so).

Other options

As mentioned above, use a renderfarm. Here's a list of renderfarms which support or even specialize in blender/cycles.

Render it overnight or in the background over the course a few weeks (perhaps using only a single core while using the computer for other things)

Bake the lighting for diffuse materials (only valid if no light sources are animated)